Vibration damping of an elastic structure can be obtained by
bonding a piezoelectric actuator onto the vibrating structure, and
by shunting the actuator to a suitable electric resonant
circuit, tuned to the structural eigenmode to be damped. The
achievable damping depends on the particular electric circuit
used. In this paper three different electric shunt circuits are
analyzed and their performances are compared. In particular, the
optimal values of the electric components belonging to each
shunt circuit and the corresponding exponential time decay rates
of the free vibrations relevant to the controlled structural
eigenmode are explicitly determined, also taking into account the
inherent structural damping. Finally, some experimental results
are reported, obtained by using two of the shunt circuits
analyzed, which are in good agreement with the theoretical
predictions.